Precalculus Semester 1 Review

Solve the equation    3x + 7 = 0

• x =  $-\frac{7}{3}$  

• x =  $\frac{7}{3}$  

• The solution set is $\left(-\infty,\infty\right)$  

• There is no solution

Find the equation for the circle with center (3,1) and passing through (- 1,4)

• $\left(x+1\right)^2+\left(y\ -\ 4\right)^2\ =\ 25$

• $\left(x+1\right)^2+\left(y\ -\ 4\right)^2\ =\ 5$

• $\left(x-3\right)^2+\left(y\ -\ 1\right)^2\ =\ 25$

• $\left(x-3\right)^2+\left(y\ -\ 1\right)^2\ =\ 5$

For the pair of functions, find the indicated sum, difference, product, or quotient.

f(x) = 8x - 7, g(x) = 5x - 3

Find ( f- g)(x)

• 3x - 4

• -3x + 4

• 3x - 10

• 13x - 10

Use the quadratic formula to find the exact solutions.
 $x^2\ -\ 10x\ +\ 61\ =\ 0$  

•  $5\pm6i$  

•  $11,\ -1$  

•  $-5\ \pm\ 6i$  

•  $10\ \pm12i$  

Find the vertex for the quadratic equation below.
 $f\left(x\right)=x^2\ -\ 16x\ +55$  

•  $\left(0,55\right)$  

•  $\left(-8,247\right)$  

•  $\left(-8,155\right)$  

•  $\left(8,-9\right)$  

Solve the following inequality and write interval notation for the solution set.
 $\left|x\ +8\right|\ <\ 4$  

•  $\left(-\infty,12\right)$  

•  $\left(-\infty,-4\right)$  

•  $\left(-12,-4\right)$  

•  $\left(-\infty,-12\right)U\left(-4,\infty\right)$  

Solve.
 $2^{3x-7}=32$  

•  $x\ =\ -2$  

•  $x\ =\ 3$  

•  $x\ =\ 4$  

•  $x\ =\ 13$  

 $2x\ +\ 3y\ =\ 25$  Find the slope and y-intercept of the equation.

•  $\frac{3}{2},\ \left(0,\frac{25}{3}\right)$  

•  $\frac{2}{3},\ \left(0,\frac{3}{25}\right)$  

•  $-\frac{3}{2},\ \left(0,\frac{3}{25}\right)$  

•  $-\frac{2}{3},\ \left(0,\frac{25}{3}\right)$  

Find the distance between the pair of points. Give an exact answer , and where appropriate, an approximation to three decimal places.  $\left(-3,6\right)\ and\ \left(-12,8\right)$  

• $\sqrt{85},\ 9.220$

• $\sqrt{221},\ 14.866$

• $\sqrt{229},\ 15.133$

• $\sqrt{421},\ 20.518$

 $\left(-4,-4\right)\ and\ \left(5,7\right)$  Find the midpoint of the segment having the given endpoints.

•  $\left(-9,-11\right)$  

•  $\left(-\frac{9}{2},-\frac{11}{2}\right)$  

•  $\left(\frac{1}{2},\ \frac{3}{2}\right)$  

•  $\left(1,3\right)$